Simplify the following expression: $\dfrac{132q}{99q^2}$ You can assume $q \neq 0$.
Explanation: $ \dfrac{132q}{99q^2} = \dfrac{132}{99} \cdot \dfrac{q}{q^2} $ To simplify $\frac{132}{99}$ , find the greatest common factor (GCD) of $132$ and $99$ $132 = 2 \cdot 2 \cdot 3 \cdot 11$ $99 = 3 \cdot 3 \cdot 11$ $ \mbox{GCD}(132, 99) = 3 \cdot 11 = 33 $ $ \dfrac{132}{99} \cdot \dfrac{q}{q^2} = \dfrac{33 \cdot 4}{33 \cdot 3} \cdot \dfrac{q}{q^2} $ $\phantom{ \dfrac{132}{99} \cdot \dfrac{1}{2}} = \dfrac{4}{3} \cdot \dfrac{q}{q^2} $ $ \dfrac{q}{q^2} = \dfrac{q}{q \cdot q} = \dfrac{1}{q} $ $ \dfrac{4}{3} \cdot \dfrac{1}{q} = \dfrac{4}{3q} $